fmincon solver for nmpc applications

-I am developing an NMPC inside a Matlab funcion in simulink by using fmincon. Could I supply the Hessian Matrix as an input in the same way as in the gradient of the cost funcion and the constraints? Because I have created a function and a introduce the command in optimotions :

options = optimoptions('fmincon', ...
    'Display', 'none', ...
    'Algorithm', 'sqp', ...                    
    'SpecifyObjectiveGradient', true, ...
    'SpecifyConstraintGradient', true, ...
    'HessianFcn',Hessfcn,...
    'ConstraintTolerance', 1e-6, ...
    'OptimalityTolerance', 1e-6, ...             % usar OptimalityTolerance en vez de FunctionTolerance
    'StepTolerance', 1e-6, ...                   % evita detenerse prematuramente
    'MaxIterations', 400);   

An the following error is displayed:

Error:'HessianFcn' is not a recognized parameter. For a list of valid name-value pair arguments, see the documentation for this function.

Function 'Variant Subsystem/NMPC Torque /NMPC Torque' (#635.1485.1950), line 49, column 11:

"optimoptions('fmincon', ..."

Launch diagnostic report.

-An another question, my NMPC is based on a single shooting formulation, could I introduce also non linear constraints such ceq and cineq as in the multiple shooting?

Answer 1

[Matt J]

FMINCON's sqp algorithm does not accept a HessianFcn parameter. You would need to switch to either trust-region-reflective or interior-point.

https://www.mathworks.com/help/optim/ug/fmincon.html?s_tid=srchtitle_support_results_1_fmincon#busog7r-options

Of these, only interior-point allows nonlinear constraints,

https://www.mathworks.com/help/optim/ug/choosing-the-algorithm.html?utm_source=chatgpt.com

so that might be preferable in view of your second question.

[Matt J]